In one conventional technique for modeling inductors, an accurate model of hysteresis loops can be obtained. See D. C. Jiles and D. L. Atherton, Journal of Magnetism and Magnetic Materials 61 (1988) at 48-60. Although the Jiles-Atherton technique is accurate, there are several disadvantages to the application of it for circuit simulation. This technique uses transcendental math functions that tend to slow simulation speed (i.e., a compute-bound process). Further, the Jiles-Atherton equations are not typically modeled in terms of parameters readily known for ferromagnetics, such as coercive force (Hc), remnant magnetization flux density (Br), and saturation flux density (Bs). Another disadvantage of Jiles-Atherton is that it has been difficult to use their method in the modeling of gapped inductors.
Another conventional approach for modeling inductors is computationally “lightweight” (i.e., no transcendental functions) but parameterized by the parameters typically known for ferromagnetics. See John Chan et al. Nonlinear Transformer Model for Circuit Simulation, IEEE Transactions on Computer-Aided Design, vol. 10, no. 4 (April 1991) at 476-482. One problem with the Chan method, however, is that asymmetric minor hysteresis loops can disadvantageously exhibit non-physical properties, such as the minor hysteresis loops extending beyond the bounds of the major hysteresis loop.
FIG. 1 illustrates the offending asymmetrical minor hysteresis loops 105 present in Chan's model. Asymmetric hysteresis loops are of two forms. Using Chan's notation of Bd as the constant of vertical translation between a minor loop branch and the corresponding branch of the major loop, if there is a minor loop with Bd less than Br that can be extended beyond the initial magnetization path to meet the turning point, then that is used for that branch of the asymmetric hysteresis loop. But if there is no such minor loop, then Chan's technique translates the lower major hysteresis loop horizontally and vertically to fit the turning point. This translation results in the offending asymmetrical minor hysteresis loops 105, which exhibit non-physical behavior in that they extend beyond the major hysteresis loop 110. The inductor appears to be saturated when traversing the offending asymmetrical minor hysteresis loops 105 because of the flatness of the slope of these loops. As one skilled in the art will appreciate, circuit simulations or other uses of Chan's model tend to produce erroneous results because the inductor appears to be saturated when it should in fact not be saturated.
What is needed is a computationally lightweight technique for modeling the ferromagnetic core of an inductor or transformer in a circuit simulator that does not exhibit non-physical behavior associated with the asymmetric minor loops. What is further needed is a technique for modeling the ferromagnetic core of an inductor or transformer that uses the typical parameters known for ferromagnetic materials.